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Fast Hermite Normal Form over ZZ

Benchmark 1: Random 200x200 single-digit matrix

Mathematica code: 

sage: mathematica.eval('a = Table[RandomInteger[{0,9}], {i,200}, {j,200}];')

sage: mathematica.eval('Timing[HermiteDecomposition[a];]')
        {98.9791, Null}

Maple code: 

> with(LinearAlgebra); n := 200: k := 9: A := RandomMatrix(n,n,generator=rand(-k..k)): time( HermiteForm(A,output=['H', 'U']) );

60.431 seconds

Sage (via PARI): 

sage: a = random_matrix(ZZ,200)
sage: time v = a.echelon_form()
CPU times: user 43.72 s, sys: 0.27 s, total: 43.98 s
Wall time: 44.36

sage: a = random_matrix(ZZ,200)
sage: z = magma(a)
sage: t = magma.cputime()
sage: time w = z.HermiteForm()
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.82
sage: magma.cputime(t)
0.68999999999999995

Benchmark 1: Random 200x200 matrix with 32-bit entries

days7/sprints/linalg (last edited 2008-11-14 13:42:08 by anonymous)